Rotating skyrmion lattices by spin torques and field or temperature gradients

Everschor, Karin; Garst, Markus; Binz, B.; Jonietz, Florian; Mühlbauer, S.; Pfleiderer, C.; Rosch, Achim

doi:10.1103/physrevb.86.054432

Cited by 193 publications

(175 citation statements)

References 39 publications

(81 reference statements)

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“…Using an approach proposed by Thiele 33 , the LLG equation can be mapped onto the translational mode in the continuum limit by assuming the rigidity of spin textures during the drift motion. One obtains 31,32 GÂðv…”

Section: Discussionmentioning

confidence: 99%

“…The first term in the left hand side of equation (3) is the Magnus force and the second one is the dissipative force. The third one is the phenomenological pinning force due to the impurities 31,32 :…”

Section: Discussionmentioning

confidence: 99%

“…We next discuss the results in the presence of impurities by taking into account F pin a0 in equations (3) and (4) 31,32 . Here we focus on the realistic value of a ¼ 0.04 as in the case of Fig.…”

Section: Discussionmentioning

confidence: 99%

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Universal current-velocity relation of skyrmion motion in chiral magnets

2013

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Current-driven motion of the magnetic domain wall in ferromagnets is attracting intense attention because of potential applications such as racetrack memory. There, the critical current density to drive the motion is B10 9 -10 12 A m À 2 . The skyrmions recently discovered in chiral magnets have much smaller critical current density of B10 5 -10 6 A m À 2 , but the microscopic mechanism is not yet explored. Here we present a numerical simulation of Landau-Lifshitz-Gilbert equation, which reveals a remarkably robust and universal currentvelocity relation of the skyrmion motion driven by the spin-transfer-torque unaffected by either impurities or nonadiabatic effect in sharp contrast to the case of domain wall or spin helix. Simulation results are analysed using a theory based on Thiele's equation, and it is concluded that this behaviour is due to the Magnus force and flexible shape-deformation of individual skyrmions and skyrmion crystal, which enable them to avoid pinning centres.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Universal current-velocity relation of skyrmion motion in chiral magnets

2013

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“…Skyrmion motion can be directly observed with Lorentz microscopy 7,10 or deduced from changes in the transport properties, permitting the construction of effective skyrmion velocity versus applied force curves that show that the skyrmion velocity increases with increasing current 20 . Other methods to move skyrmions include the use of temperature gradients [27][28][29][30][31] , electric fields 32,33 , and coupling to a magnetic tip 15 .…”

Section: Introductionmentioning

confidence: 99%

Quantized transport for a skyrmion moving on a two-dimensional periodic substrate

2015

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We examine the dynamics of a skyrmion moving over a two-dimensional periodic substrate utilizing simulations of a particle-based skyrmion model. We specifically examine the role of the non-dissipative Magnus term on the driven motion and the resulting skyrmion velocity-force curves. In the overdamped limit, there is a depinning transition into a sliding state in which the skyrmion moves in the same direction as the external drive. When there is a finite Magnus component in the equation of motion, a skyrmion in the absence of a substrate moves at an angle with respect to the direction of the external driving force. When a periodic substrate is added, the direction of motion or Hall angle of the skyrmion is dependent on the amplitude of the external drive, only approaching the substrate-free limit for higher drives. Due to the underlying symmetry of the substrate the direction of skyrmion motion does not change continuously as a function of drive, but rather forms a series of discrete steps corresponding to integer or rational ratios of the velocity components perpendicular ( V ⊥ ) and parallel ( V || ) to the external drive direction: V ⊥ / V || = n/m, where n and m are integers. The skyrmion passes through a series of directional locking phases in which the motion is locked to certain symmetry directions of the substrate for fixed intervals of the drive amplitude. Within a given directionally locked phase, the Hall angle remains constant and the skyrmion moves in an orderly fashion through the sample. Signatures of the transitions into and out of these locked phases take the form of pronounced cusps in the skyrmion velocity versus force curves, as well as regions of negative differential mobility in which the net skyrmion velocity decreases with increasing external driving force. The number of steps in the transport curve increases when the relative strength of the Magnus term is increased. We also observe an overshoot phenomena in the directional locking, where the skyrmion motion can lock to a Hall angle greater than the clean limit value and then jump back to the lower value at higher drives. The skyrmion-substrate interactions can also produce a skyrmion acceleration effect in which, due to the non-dissipative dynamics, the skyrmion velocity exceeds the value expected to be produced by the external drive. We find that these effects are robust for different types of periodic substrates. Using a simple model for a skyrmion interacting with a single pinning site, we can capture the behavior of the change in the Hall angle with increasing external drive. When the skyrmion moves through the pinning site, its trajectory exhibits a side step phenomenon since the Magnus term induces a curvature in the skyrmion orbit. As the drive increases, this curvature is reduced and the side step effect is also reduced. Increasing the strength of the Magnus term reduces the range of impact parameters over which the skyrmion can be captured by a pinning site, which is one of the reasons that strong Magnus force effects reduce the...

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“…Electric fields as low as 10 2 V/m can induce drift velocities v H ∼ 0.1 mm/s, comparable to skyrmions driven by conduction electrons in metallic systems 42 , according to the STT mechanism (Ref. 26,27,32,43,44 and references therein). In the system under consideration the skyrmionic material is insulating and the the surface spectrum of TI is gapped away from the skyrmion, which makes the STT mechanism unimportant.…”

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confidence: 99%

Charged skyrmions on the surface of a topological insulator

et al. 2015

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We consider the interplay between magnetic skyrmions in an insulating thin film and the Dirac surface states of a 3D topological insulator (TI), coupled by proximity effect. The magnetic texture of skyrmions can lead to confinement of Dirac states at the skyrmion radius, where out of plane magnetization vanishes. This confinement can result in charging of the skyrmion texture. The presence of bound states is robust in an external magnetic field, which is needed to stabilize skyrmions. It is expected that for relevant experimental parameters skyrmions will have a few bound states that can be tuned using an external magnetic field. We argue that these charged skyrmions can be manipulated directly by an electric field, with skyrmion mobility proportional to the number of bound states at the skyrmion radius. Coupling skyrmionic thin films to a TI surface can provide a more direct and efficient way of controlling skyrmion motion in insulating materials. This provides a new dimension in the study of skyrmion manipulation.

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Rotating skyrmion lattices by spin torques and field or temperature gradients

Cited by 193 publications

References 39 publications

Universal current-velocity relation of skyrmion motion in chiral magnets

Universal current-velocity relation of skyrmion motion in chiral magnets

Quantized transport for a skyrmion moving on a two-dimensional periodic substrate

Charged skyrmions on the surface of a topological insulator

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